The purpose of this project is to develop new statistical methods for, and to apply new and existing statistical techniques in, the analysis of data from laboratory animal studies. Special emphasis is placed on the type of data arising in the National Toxicology Program (NTP) carcinogenesis bioassays. Much of my research time is spent working on new statistical solutions to practical problems which are important to NTP scientists. In addition, some of my research time is devoted to applying these new procedures to the specific data which originally motivated the work on methods development. Finally, the remainder of my research time is spent applying existing statistical procedures, sometimes in novel ways, to data collected by collaborators here at the National Institute of Environmental Health Sciences (NIEHS). Some of my methodological research is summarized in Dr. Shyamal Peddada's project entitled 'Statistical Theory and Methodology With Applications to Toxicology' (Z01-ES-101744) and some of my collaborative research is summarized in Dr. Peddada's project entitled 'NIEHS Statistical Consulting Service' (Z01-ES-045005). However, the majority of my research, as well as some of Dr. David Dunson's research, relates primarily to the development of new methods in two areas: (1) inference about shape-constrained hazard functions and (2) accounting for body weight in causal inferences about tumor incidence. Both methods are developed in a Bayesian framework and use Markov Chain Monte Carlo (MCMC) computational techniques. These two areas of research are described in more detail below.